A Method to Determine the Fractal Roughness Parameter from Surface Profiles Generated by the WM Function

2013 ◽  
Vol 341-342 ◽  
pp. 329-332 ◽  
Author(s):  
Li Wang ◽  
Yang Xiang
Keyword(s):  
Fractal Dimension ◽  
Numerical Scheme ◽  
Function Method ◽  
Roughness Parameter ◽  
Surface Profile ◽  
Reasonable Accuracy ◽  
Characteristic Parameters ◽  
Fractal Surface ◽  
Fractal Roughness ◽  
Surface Profiles

The fractal surface profile can usually be represented by WM function, A fractal dimension and a fractal roughness parameter are very important characteristic parameters in WM function. Usually, fractal scaling parameter γ was set to equal to 1.5, fractal dimension can be determined by the structure function method, but the accurately identification of the fractal roughness parameter is still a problem. In the present study, a simply numerical scheme with clear routine was developed to determine the fractal roughness parameter, and the fractal roughness parameter were recovered with reasonable accuracy from the numerically generated rough surface profile based WM function.

Experimental and Theoretical Studies of the Fractal Scaling Parameter and the Lateral Scale Dependence of the Asperity Interference

2007 ◽  
Author(s):  
Shao Wang ◽  
Yi Hui Leong
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Numerical Scheme ◽  
Surface Profile ◽  
Density Data ◽  
Fractal Scaling ◽  
Scaling Parameter ◽  
Power Spectral ◽  
Surface Profiles ◽  
The Difference

The fractal scaling parameter was released in a recent study from its artificially assigned constant value to become a measurable parameter for simulated surface profiles. In the present study, this concept was extended to develop schemes for determining the fractal scaling parameter from experimental power spectral density data. The difference in the trends of peaks has been observed between experimental power spectral density data and those of the Weierstrass-Mandelbrot function. A modified W-M function was proposed based on a peak splitting behavior of the power spectrum. To verify a relationship between the interference and lateral length scale for asperities, which is commonly assumed in fractal modeling, a numerical scheme was developed to truncate measured surface profiles for finding asperity interferences for microcontacts of various sizes. This relationship was confirmed by the favorable results from a comparison of the power values obtained from truncation of a surface profile to those obtained by using the fast Fourier transform. A numerical scheme was developed to generate random power spectral density curves and fractal surface profiles for given values of the fractal scaling parameter.

scholarly journals Interval estimation for contact stiffness of bolted joint with uncertain parameters

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401988370 ◽  
Author(s):  
Yongsheng Zhao ◽  
Hongchao Wu ◽  
Congbin Yang ◽  
Zhifeng Liu ◽  
Qiang Cheng
Keyword(s):  
Fractal Dimension ◽  
Contact Surface ◽  
Contact Stiffness ◽  
Interval Estimation ◽  
Roughness Parameter ◽  
Normal Pressure ◽  
Bolted Joints ◽  
Uncertain Parameters ◽  
Fractal Parameters ◽  
Fractal Roughness

Bolted joints are elements used to create resistant assemblies in the mechanical system, whose overall performance is greatly affected by joints’ contact stiffness. Most of the researches on contact stiffness are based on certainty theory whereas in real applications the uncertainty characterizes the parameters such as fractal dimension D and fractal roughness parameter G. This article presents an interval estimation theory to obtain the stiffness of bolted joints affected by uncertain parameters. Topography of the contact surface is fractal featured and determined by fractal parameters. Joint stiffness model is built based on the fractal geometry theory and contact mechanics. Topography of the contact surface of bolted joints is measured to obtain the interval of uncertain fractal parameters. Equations with interval parameters are solved to acquire the interval of contact stiffness using the Chebyshev interval method. The relationship between the interval of contact stiffness and the uncertain parameters, that is, fractal dimension D, fractal roughness parameter G, and normal pressure, can be obtained. The presented model can be used to estimate the interval of stiffness for bolted joints in the mechanical systems. The results can provide theoretical reference for the reliability design of bolted joints.

THE THREE-POINT SINUOSITY METHOD FOR CALCULATING THE FRACTAL DIMENSION OF MACHINED SURFACE PROFILE

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550016 ◽  
Author(s):  
YUANKAI ZHOU ◽  
YAN LI ◽  
HUA ZHU ◽  
XUE ZUO ◽  
JIANHUA YANG
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Structural Complexity ◽  
Variation Method ◽  
Real Surface ◽  
Machined Surface ◽  
Box Counting ◽  
Scaling Region ◽  
Fractal Characteristics ◽  
Surface Profiles

The three-point sinuosity (TPS) method is proposed to calculate the fractal dimension of surface profile accurately. In this method, a new measure, TPS is defined to present the structural complexity of fractal curves, and has been proved to follow the power law. Thus, the fractal dimension can be calculated through the slope of the fitted line in the log–log plot. The Weierstrass–Mandelbrot (W–M) fractal curves, as well as the real surface profiles obtained by grinding, sand blasting and turning, are used to validate the effectiveness of the proposed method. The calculation values are compared to those obtained from root-mean-square (RMS) method, box-counting (BC) method and variation method. The results show that the TPS method has the widest scaling region, the least fit error and the highest accuracy among the methods examined, which demonstrates that the fractal characteristics of the fractal curves can be well revealed by the proposed method.

Classification and Recognition of Plant Leaf Based on Neural Networks

2011 ◽  
Vol 464 ◽  
pp. 38-42 ◽  
Author(s):  
Ping Ye ◽  
Gui Rong Weng
Keyword(s):  
Neural Networks ◽  
Fractal Dimension ◽  
Recognition Rate ◽  
Image Binarization ◽  
Characteristic Parameters ◽  
Moment Invariant ◽  
Plant Leaf ◽  
The Neural Networks ◽  
Novel Method ◽  
The Moment

This paper proposed a novel method for leaf classification and recognition. In the method, the moment invariant and fractal dimension were regarded as the characteristic parameters of the plant leaf. In order to extract the representative characteristic parameters, pretreatment of the leaf images, including RGB-gray converting, image binarization and leafstalk removing. The extracted leaf characteristic parameters were further utilized as training sets to train the neural networks. The proposed method was proved effectively to reach a recognition rate about 92% for most of the testing leaf samples

Experimental Observation of Fractal-Regular Surfaces and a Transformation Scheme for Extracting Fractal Parameters

2005 ◽  
Author(s):  
Shao Wang ◽  
Wai Kin Chan
Keyword(s):  
Silicon Wafer ◽  
Roughness Parameter ◽  
Hard Disk ◽  
Spectral Density Function ◽  
Power Spectral ◽  
Fractal Parameters ◽  
Asperity Contacts ◽  
Fractal Roughness ◽  
Magnetic Hard Disk ◽  
Wafer Surfaces

To account for the effects of asperity contacts at various length scales, it is appropriate to characterize an engineering surface as a fractal-regular surface. In spite of significant theoretical advancement, there is a desperate need for experimental verification of the theory of fractal-regular surfaces and a consistent scheme of obtaining the fractal parameters. In the present study, the existence of a fractal region and a regular-shape region in the power spectral density function for fractal-regular surfaces was confirmed experimentally, for the first time, with data obtained from magnetic hard disk and silicon wafer surfaces. A novel scheme involving a variable transformation was developed to extract fractal parameters. This scheme was validated by accurate recovery of fractal parameters from simulated surfaces. The fractal dimension, the fractal roughness parameter and the fractal domain length were found for magnetic hard disk and silicon wafer surfaces.

scholarly journals A Simple Model to Predict Machined Depth and Surface Profile for Picosecond Laser Surface Texturing

2018 ◽  
Vol 8 (11) ◽  
pp. 2111 ◽  
Author(s):  
Jieyu Xian ◽  
Xingsheng Wang ◽  
Xiuqing Fu ◽  
Zhengwei Zhang ◽  
Lu Liu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Surface Texturing ◽  
Surface Profile ◽  
Picosecond Laser ◽  
Scanning Speed ◽  
Laser Surface ◽  
Laser Surface Texturing ◽  
Micro Channels ◽  
Surface Profiles ◽  
Simulation Parameters

A simple mathematical model was developed to predict the machined depth and surface profile in laser surface texturing of micro-channels using a picosecond laser. Fabrication of micro-craters with pulse trains of different numbers was initially performed. Two baseline values from the created micro-craters were used to calculate the estimated simulation parameters. Thereafter, the depths and profiles with various scanning speeds or adjacent intervals were simulated using the developed model and calculated parameters. Corresponding experiments were conducted to validate the developed mathematical model. An excellent agreement was obtained for the predicted and experimental depths and surface profiles. The machined depth decreased with the increase of scanning speed or adjacent interval.

scholarly journals Influence of gas detonation spraying parameters on the geometrical structure of Fe-Al intermetallic protective coatings

2019 ◽  
Author(s):  
Tomasz Chrostek ◽  
Mirosław Bramowicz ◽  
Kazimierz Rychlik ◽  
Wojtkowiak Adam ◽  
Cezary Senderowski
Keyword(s):  
Fractal Dimension ◽  
Geometric Structure ◽  
Geometrical Structure ◽  
Protective Coatings ◽  
Sampling Rate ◽  
Roughness Parameter ◽  
Powder Injection ◽  
Science Center ◽  
Detonation Spraying ◽  
Gas Detonation

The paper presents the results of an investigation and analysis of the geometrical structure of Fe-Al intermetallic protective coatings sprayed under specified gun detonation spraying (GDS) conditions. As GDS variable parameters there were applied two different barrel lengths and two powder injection position (PIP) at the moment of spark detonation as well as two different number of GDS shots with 6.66 Hz frequency. The measurements of the surface's profile were carried out through means of contact profilometry, in which case TOPO-01 system and Mitutoyo SJ 210 profilometer were applied. On the basis of the measurements conducted the analysis of in two-dimensional (2D) and spatial (3D) systems was made possible. The authors assumed that roughness can be considered as a non-stationary parameter of variance of surface amplitude, which is highly dependent on the sampling rate and length of an elementary segments. Therefore, the changes in the amplitude parameters and functional properties of the surface at different lengths of measuring segments (ln), respectively: 1.25, 4 and 12.5 mm, were analyzed. In the analysis of the degree of development of the geometric structure of the surface, the RMS (Root Mean Square) fractal method was used, with an assessment of the geometric structure of the surface stretched over several size levels, taking into account the correlation between the roughness parameter Rq, the measuring length (ln) and the fractal dimension (D). The application of the RMS method with the determination of the fractal dimension (D) allowed for the characterization of the geometric structure of intermetallic Fe-Al protective coatings detonation sprayed under specific conditions of the GDS process - based on the surface roughness profiles of different measured length (ln). Research undertaken within the framework of project No. 2015/19 / B / ST8 / 02000 subsidized by the National Science Center of Poland.

Geometrical consideration for mechanical contact between rolling circle and surface roughness as an improvement to the surface profile

2021 ◽  
Vol 15 (1) ◽  
pp. 7846-7859
Author(s):  
Tsuyoshi Shimizu ◽  
Yasutake Hramiishi ◽  
Takaaki Ishii ◽  
Yuzairi Abdul Rahim ◽  
Mohd Fadzil Ali Ahmad ◽  
...  
Keyword(s):  
Contact Point ◽  
Surface Profile ◽  
Displacement Sensor ◽  
Nose Radius ◽  
Rolling Circle ◽  
Actual Surface ◽  
Contact Type ◽  
Measurement Surface ◽  
Surface Profiles ◽  
Tip Radius

This paper describes measurement methods of surface profiles that improve contact-type displacement sensor outputs by focusing on the contact point between the sphere tip of the sensor and the rough surface. We examined the geometry of a surface profile model and compared measurements using various methods with the measurement using a roughness meter. The spherical tip of the contact type displacement sensor touches the measurement surface and detects the displacement. The sphere tip radius of a typical contact-type displacement sensor ranges from 1–3 mm, causing the roughness curve to be “filtered” by the radius of the sphere.  Three methods for estimating the valley portion of the surface profile are evaluated in this study: a) linear approximation of the concave portion of the surface profile, b) function approximation of the concave portion, and c) using the known nose radius of the machining tool. The following sphere tip radii were used to measure actual surface profiles: 0.25 mm, 0.5 mm, 1.0 mm and 1.5 mm. Given the conditions of the experimental model, we found that surface profiles with a roughness that approximates a predictable curve can be measured with a high degree of accuracy.

scholarly journals How surface stress transforms surface profiles and adhesion of rough elastic bodies

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200477
Author(s):  
Chung-Yuen Hui ◽  
Zezhou Liu ◽  
Nicolas Bain ◽  
Anand Jagota ◽  
Eric R. Dufresne ◽  
...  
Keyword(s):  
Surface Stress ◽  
Periodic Structures ◽  
Surface Profile ◽  
Initial Surface ◽  
One Dimensional ◽  
Patterned Substrate ◽  
Soft Solids ◽  
Elastic Bodies ◽  
Surface Profiles ◽  
Qualitative Changes

The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.

Stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities

2019 ◽  
Vol 72 (1) ◽  
pp. 128-135 ◽  
Author(s):  
Hongxu Chen ◽  
Qin Yin ◽  
Guanhua Dong ◽  
Luofeng Xie ◽  
Guofu Yin
Keyword(s):  
Elastic Deformation ◽  
Contact Stiffness ◽  
Roughness Parameter ◽  
Experimental Results ◽  
Content Type ◽  
Elastoplastic Contact ◽  
Proposed Model ◽  
Stiffness Model ◽  
Fractal Roughness ◽  
Deformation Ratio

Purpose The purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities. Design/methodology/approach The proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities. Findings A revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model. Originality/value The contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.

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